3) The finite complement topology on a set X is the collection of subsets U such that X-U is either a finite set or is all of X. Show that this collection satisfies the axioms of a topology. Definition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.
3) The finite complement topology on a set X is the collection of subsets U such that X-U is either a finite set or is all of X. Show that this collection satisfies the axioms of a topology. Definition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.3: Properties Of Composite Mappings (optional)
Problem 9E: Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a...
Related questions
Question

Transcribed Image Text:3) The finite complement topology on a set X is the collection of subsets U such that
X-U is either a finite set or is all of X. Show that this collection satisfies the axioms
of a topology.

Transcribed Image Text:Definition: A topology on a set X is a collection T of subsets of X having the following
properties.
(1) Both the empty set and X itself are elements of T.
(2) The union of an arbitrary collection of elements of T is an element of T.
(3) The intersection of a finite number of elements of T is an element of T.
A set X with a specified topology T is called a topological space. The subsets of X that are
members of are called the open sets of the topological space.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps

Recommended textbooks for you

Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,

Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning

Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,

Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning